SOLUTION: You are standing 16 feet from a circular swimming pool. The distance from you to a point of tangency is 25 feet. What is the approximate diameter of the pool?

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Question 859243: You are standing 16 feet
from a circular swimming pool. The distance
from you to a point of tangency is 25 feet.
What is the approximate diameter of the
pool?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Hint: Draw the picture to get





You are at point D. The length of CD is 16 feet. The center of the circle is point A. Point B is the point of tangency of line BD (angle ABD = 90 degrees) and segment BD = 25 feet.


The radius of the circle is unknown for now. We'll call it r


Now use the Pythagorean Theorem


a%5E2+%2B+b%5E2=c%5E2


r%5E2+%2B+25%5E2=%2816%2Br%29%5E2


r%5E2+%2B+625=256%2B32r%2Br%5E2


r%5E2+%2B+625-r%5E2=256%2B32r%2Br%5E2-r%5E2 Subtract r%5E2 from both sides.


625=256%2B32r


I'll let you finish up.


Keep in mind that d+=+2r where d is the diameter of the circle.